Linear programming model for business optimization

Deterministic Modeling: Linear Optimization With Applications

Multi-objective optimization using Linear Algebra

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Linear programming (LP) is to find the maximum or minimum of a linear objective under linear constraints. It is a mathematical or analytical optimization model which consists of an objective function and a set of constraints in the form of a system of equations or inequalities. The mathematical model describes the behavior of the measure of effectiveness which is called the objective function.

However, in practice, mathematical equations rarely capture the precise relationship between all system variables and the measure of effectiveness. Instead, we must strive to identify the variables that most significantly affect the measure of effectiveness, and then attempt to logically define the mathematical relationship between these variables and the measure of effectiveness. This mathematical relationship is the objective function that is used to evaluate the performance.

Formulation of a meaningful objective function is an iterative process and involves a tedious and frustrating task which comes with many failures. Failure could result because we chose the wrong set of variables, because we fail to…